Steinhaus' Billiard Ball Loop

A billiard path is a polygon with vertices on the faces of a polyhedron such that if two segments meet at a vertex on a face , the plane through them is perpendicular to and the angle they form is bisected by the normal to at . A billiard ball loop is a closed billiard path.

This Demonstration shows a billiard ball loop in a cube discovered by Hugo Steinhaus. Each vertex lies at a distance one-third of the cube's edge length from two edges. The projection of the loop perpendicular to any face of the cube is a rectangle, and the projection along one of the main diagonals of the cube is a regular hexagon.